Module 2 · SSC CGL Reasoning
Syllogism
Venn diagrams, definite/possible conclusions.
Venn Diagrams · Conclusions
Learning Objectives
- Understand the fundamental concepts of Syllogism
- Apply key formulas and techniques to solve problems
- Practice with exam-level questions to build speed and accuracy
Key Concepts
Introduction to Syllogism
Syllogism is the most scoring topic in SSC CGL Reasoning. In Tier 1, 2-3 questions appear; in Tier 2, 3-4 questions appear. With the right approach, you can solve ANY syllogism question in under 20 seconds — guaranteed 100% accuracy.
SSC CGL Exam Pattern (All Variants)
Over the last 5 years, SSC has asked syllogism in these formats:
- Type 1 — Direct Statements: 2-3 statements given, find which conclusions follow. [Most common — 60% of questions]
- Type 2 — Possibility Conclusions: Statements with "can be", "may be", "possibly" in conclusions. [20% of questions]
- Type 3 — Either-Or Cases: Complementary pair conclusions where exactly one must be true. [10% of questions]
- Type 4 — Coded Syllogisms: Statements coded with symbols like A % B means "All A are B". [10% — increasing trend since 2023]
- Type 5 — Only / Only a few Statements: "Only A are B" means "All B are A". [Introduced in 2024]
The Lightning-Fast Method (15 Seconds per Question)
Method: The 3-Step Elimination
Step 1: Draw the possible Venn Diagrams (maximum 2 possibilities).
Step 2: Check each conclusion against BOTH diagrams.
Step 3: If a conclusion is TRUE in ALL diagrams → it follows. If FALSE in ANY → it doesn't follow.
âš¡ Speed Trick #1: The 100-50 Rule
100% statements (All, No) give DEFINITE conclusions. 50% statements (Some, Some Not) give POSSIBILITY conclusions. When a conclusion has "Some" and the statements are all "All/No", the conclusion is usually FALSE because "All" doesn't guarantee "Some" (the set could be empty).
âš¡ Speed Trick #2: Rahul's 8 Rules (Memorize These!)
When combining TWO statements:
1. All + All = All (A→B, B→C => A→C)
2. All + No = No (A→B, B X C => A X C)
3. All + Some = No Conclusion (A→B, B∼C => nothing definite about A↔C)
4. No + All = Some Not Reverse (A X B, B→C => Some C are not A)
5. No + No = No Conclusion (A X B, B X C => no relation)
6. Some + All = Some (A∼B, B→C => A∼C)
7. Some + No = Some Not (A∼B, B X C => Some A are not C)
8. Some + Some = No Conclusion (A∼B, B∼C => no relation)
1. All + All = All (A→B, B→C => A→C)
2. All + No = No (A→B, B X C => A X C)
3. All + Some = No Conclusion (A→B, B∼C => nothing definite about A↔C)
4. No + All = Some Not Reverse (A X B, B→C => Some C are not A)
5. No + No = No Conclusion (A X B, B X C => no relation)
6. Some + All = Some (A∼B, B→C => A∼C)
7. Some + No = Some Not (A∼B, B X C => Some A are not C)
8. Some + Some = No Conclusion (A∼B, B∼C => no relation)
âš¡ Speed Trick #3: The Either-Or Detective
Either-Or follows when ALL three conditions are met:
1. Both conclusions use the SAME subjects and predicates.
2. One conclusion is POSITIVE, the other is NEGATIVE.
3. Individually, both are FALSE (can't follow from statements).
Example: Statements: Some A are B. No B is C.
Conclusions: I. All A are C. II. No A is C.
Both are FALSE individually, but one MUST be true → Either-Or follows.
1. Both conclusions use the SAME subjects and predicates.
2. One conclusion is POSITIVE, the other is NEGATIVE.
3. Individually, both are FALSE (can't follow from statements).
Example: Statements: Some A are B. No B is C.
Conclusions: I. All A are C. II. No A is C.
Both are FALSE individually, but one MUST be true → Either-Or follows.
âš¡ Speed Trick #4: Coded Syllogism Decoder
SSC uses these codes (2023-24 pattern):
A % B = All A are B
A @ B = No A is B
A # B = Some A are B
A $ B = Some A are not B
A & B = Only A are B (All B are A)
Memorize these as: %=All, @=No, #=Some, $=SomeNot, &=Only
A % B = All A are B
A @ B = No A is B
A # B = Some A are B
A $ B = Some A are not B
A & B = Only A are B (All B are A)
Memorize these as: %=All, @=No, #=Some, $=SomeNot, &=Only
All 20 Question Variants with Lightning-Fast Solutions
Variant 1: Standard 2-Statement Syllogism
Variant 1 — Solved in 10 seconds
Statements:
All dogs are mammals. No mammal is a reptile.
Conclusions:
I. No dog is a reptile.
II. Some mammals are dogs.
Which follow(s)?
All dogs are mammals. No mammal is a reptile.
Conclusions:
I. No dog is a reptile.
II. Some mammals are dogs.
Which follow(s)?
⚡ Lightning Solution: Using Rule #2 (All+No=No): "All dogs are mammals" + "No mammal is a reptile" → "No dog is a reptile". Conclusion I follows. Conclusion II: Since ALL dogs are mammals, at least SOME mammals are dogs → follows. Both I and II follow. Time: 8 seconds.
Variant 2: Three-Statement Syllogism
Variant 2 — Chain Method
Statements:
All A are B. All B are C. No C is D.
Conclusions:
I. No A is D.
II. Some C are B.
III. No B is D.
All A are B. All B are C. No C is D.
Conclusions:
I. No A is D.
II. Some C are B.
III. No B is D.
⚡ Lightning Solution: Chain: A→B→C→(no)D. So A→(no)D → I follows. Since all B are C, SOME C are B → II follows. B→C→(no)D means No B is D → III follows. All three follow. Time: 12 seconds.
Variant 3: Possibility Conclusions
Variant 3 — "Can Be" Cases
Statements:
Some fruits are sweet. All sweet things are tasty.
Conclusions:
I. All fruits are tasty.
II. Some fruits are tasty.
III. All tasty things could be fruits (possibility).
Some fruits are sweet. All sweet things are tasty.
Conclusions:
I. All fruits are tasty.
II. Some fruits are tasty.
III. All tasty things could be fruits (possibility).
⚡ Lightning Solution: I — False (Some fruits are sweet, sweet→tasty, but some fruits might not be sweet → not all fruits are tasty). II — True (Some fruits are sweet → sweet→tasty → those fruits are tasty). III — TRUE (Possibility: it's possible all tasty things are fruits — no statement contradicts this). For possibility conclusions, if it CAN'T be proven false, it follows! Time: 14 seconds.
Variant 4: Either-Or Case
Variant 4 — Complementary Pair
Statements:
Some pens are pencils. No pencil is an eraser.
Conclusions:
I. All pens are erasers.
II. No pen is an eraser.
Some pens are pencils. No pencil is an eraser.
Conclusions:
I. All pens are erasers.
II. No pen is an eraser.
âš¡ Lightning Solution: Check if Either-Or applies:
1) Same subject (pen) and predicate (eraser) — YES
2) One positive (All are), one negative (No) — YES
3) Both individually FALSE: I — obviously false (some pens are pencils → no pencil is eraser → some pens NOT erasers). II — also false (some pens are pencils, but some pens might be erasers through another relation). Since both are false individually but one MUST be true → Either-Or follows. Time: 15 seconds.
1) Same subject (pen) and predicate (eraser) — YES
2) One positive (All are), one negative (No) — YES
3) Both individually FALSE: I — obviously false (some pens are pencils → no pencil is eraser → some pens NOT erasers). II — also false (some pens are pencils, but some pens might be erasers through another relation). Since both are false individually but one MUST be true → Either-Or follows. Time: 15 seconds.
Variant 5: Only Statements
Variant 5 — "Only A are B"
Statements:
Only doctors are engineers. Some engineers are rich.
Conclusions:
I. All engineers are doctors.
II. Some doctors are rich.
Only doctors are engineers. Some engineers are rich.
Conclusions:
I. All engineers are doctors.
II. Some doctors are rich.
⚡ Lightning Solution: "Only doctors are engineers" means "All engineers are doctors" (reversal). So: All engineers are doctors. Some engineers are rich → Some doctors are rich (Some+All=Some). Conclusion I follows (direct translation). Conclusion II follows. Time: 10 seconds.
Variant 6: Coded Syllogism
Variant 6 — Symbol Based
Statements:
A % B, B @ C, C # D
(where %=All, @=No, #=Some)
Conclusions:
I. A @ C
II. C # A (possibility)
A % B, B @ C, C # D
(where %=All, @=No, #=Some)
Conclusions:
I. A @ C
II. C # A (possibility)
âš¡ Lightning Solution: Decode: All A are B. No B is C. Some C are D.
I: A→B, B×C → All+No = No → A×C → No A is C → follows.
II: Some C are not A is definitely true, but "Some C are A" as possibility: it's possible? NO, because A×C (No A is C) means no C can be A even as possibility. False. Time: 14 seconds.
I: A→B, B×C → All+No = No → A×C → No A is C → follows.
II: Some C are not A is definitely true, but "Some C are A" as possibility: it's possible? NO, because A×C (No A is C) means no C can be A even as possibility. False. Time: 14 seconds.
More Variants (7-20)
Variant 7: "Only a Few" Statements
"Only a few A are B" means "Some A are B AND Some A are not B" (both are true).
Variant 8: 4-Statement Chain
Handle by combining 2 at a time using Rahul's rules.
Variant 9: Negative Conclusions
"Some A are not B" is concluded when: any part of A is definitely outside B.
Variant 10: Definite vs Possibility
Words like "some", "all", "no" → definite. Words like "can", "may", "possibly" → possibility.
âš¡ Speed Trick #5: The Complement Rule
If a conclusion is FALSE, its complement MIGHT be true as a possibility. Complement pairs: All↔Some Not, No↔Some, Some↔No, Some Not↔All. Example: If "All A are B" is false, then "Some A are not B" must be true.
âš¡ Speed Trick #6: The Minimum Diagram Rule
Always draw the MINIMUM overlapping Venn diagram first. Only add more overlaps when forced by statements. Most SSC syllogisms can be solved with just one correct diagram.
Solved Examples — 15 Quick Solutions
All 15 examples cover every variant asked in SSC CGL 2019-2025.
Example 1
All cats are animals. No animal is a stone. → No cat is a stone. (All+No=No)
Example 2
Some pens are tables. All tables are chairs. → Some pens are chairs. (Some+All=Some)
Example 3
No book is a copy. All copies are pages. → Some pages are not books. (No+All=Some Not Reverse)
Example 4
All roses are flowers. Some flowers fade quickly. → No conclusion about roses.
Example 5
No A is B. No B is C. → No conclusion about A and C.
Example 6
Some A are B. Some B are C. → No conclusion about A and C.
Example 7
All A are B. Some A are C. → Some B are C (true). Some C are B (true).
Example 8
Only rich are happy. → All happy are rich.
Example 9
All dogs bark. No cat barks. → No dog is a cat. (No+All trick)
Example 10
Some teachers are strict. All strict people are respected. → Some teachers are respected.
Example 11
No honest person is corrupt. Some politicians are honest. → Some politicians are not corrupt.
Example 12
All squares are rectangles. All rectangles are polygons. → All squares are polygons.
Example 13
Some cups are plates. No plate is a bowl. → Some cups are not bowls.
Example 14
All poets are writers. Some writers are not famous. → No conclusion about poets.
Example 15
A % B, B & C, C @ D → All A are B. All C are B (since B & C = Only B are C = All C are B). No C is D. So: A→B, C→B → No direct A-C relation. But B∼C (some overlap exists). Conclusion: No A is D? Can't say. Some B are not D? Yes (C is inside B, C×D → Some B are not D).
Advanced Problems — Tier 2 Level (8 Problems)
Advanced 1
Statements: All metals are solids. All solids are liquids. No liquid is a gas. Conclusions: I. No metal is a gas. II. Some liquids are solids. III. No solid is a gas.
All three follow. Chain: Metal→Solid→Liquid→(no)Gas.
Advanced 2 — Coded
A % B, C @ D, B # C. Which is true? a) A % C b) A @ C c) A # C d) A $ C
All A are B, No C is D, Some B are C. A→B∼C → Some A are C? Not necessarily (A could be in the part of B that doesn't overlap with C). Since A→B and B∼C, we get Some B that are C exist, but A might or might not be those B. So no definite A-C relation → none follows.
Advanced 3
Only a few stars are planets. All planets are moons. Some moons are asteroids. Find which follow: I. Some stars are not planets. II. All moons being stars is a possibility.
"Only a few stars are planets" = Some stars are planets AND Some stars are not planets. I → TRUE (direct). II → Possible? Moons could all be stars as long as it doesn't contradict "only a few stars are planets". If all moons are stars, then planets (subset of moons) are also stars — but that would contradict "only a FEW stars are planets". So FALSE.
Advanced 4 — 5 Statements
All X are Y. No Y is Z. Some Z are W. All W are V. No V is U. Conclusions about X and U?
X→Y, Y×Z → X×Z (No X is Z). Z∼W, W→V → Some Z are V. But X×Z and Z∼V means no direct X-V relation. X→Y→(no)Z→(some)W→V. From X to V: X→Y (all), Y×Z (no), Z∼W (some), W→V (all). The chain stops at Y×Z — X can't reach Z, so X can't reach V. No definite conclusion.
âš¡ Speed Trick #7: The Coded Syllogism Shortcut
For coded syllogisms, convert ALL statements to their English form first before combining. Write them as arrows: A→B (All A are B), A×B (No A is B), A∼B (Some A are B). Then use the 8 rules. This takes 5 extra seconds but eliminates errors.
Common Mistakes & How to Avoid (18 Mistakes)
- Mistake 1: Assuming "Some" implies "All" — FALSE. Some A are B does NOT mean all A are B.
- Mistake 2: Applying rules in wrong order — Always combine statements from TOP to BOTTOM.
- Mistake 3: Forgetting that "All A are B" also means "Some B are A" (conversion is valid for All → Some).
- Mistake 4: Thinking "No A is B" means "No B is A" — This IS valid (conversion of No).
- Mistake 5: "Some A are B" conversion → "Some B are A" — VALID.
- Mistake 6: "Some A are not B" conversion → NOT valid. "Some A are not B" doesn't tell us anything about B.
- Mistake 7: Missing Either-Or when it applies — check the 3 conditions.
- Mistake 8: Considering "possibility" as definite — if it says "can be", check if it's IMPOSSIBLE, not if it's definite.
- Mistake 9: Forgetting "Only A are B" = "All B are A".
- Mistake 10: Ignoring "Only a few" = Some + Some Not.
- Mistake 11: Drawing too many Venn diagrams — one correct diagram is enough.
- Mistake 12: Not checking BOTH possible diagrams (if multiple exist).
- Mistake 13: Confusing complementary pair "Some + Some Not" with "All + Some Not".
- Mistake 14: Marking "Follows" when a conclusion is true in ONE diagram but false in another.
- Mistake 15: Spending >30 seconds — if stuck, use elimination.
- Mistake 16: Not practicing coded syllogisms — this is the NEW hot trend.
- Mistake 17: Misreading "Some A are B, Some B are C" → No conclusion about A-C.
- Mistake 18: Forgetting that a conclusion with "All" can be true even when "Some" is also possible.
Pro Tips from SSC Toppers
🆠Topper Secret #1
In SSC CGL Tier 1, 80% of syllogism questions use only 2 statements. Master the 8 combination rules and you'll solve them in under 10 seconds.
🆠Topper Secret #2
For coded syllogisms, write the arrow notation on rough paper: → (All), × (No), ∼ (Some). Then combine. This visual method is 50% faster than mental processing.
🆠Topper Secret #3
When checking Either-Or, first check if the two conclusions are COMPLEMENTARY (same subject & predicate, opposite qualifiers). If yes, check if BOTH are false individually. If both false → Either-Or follows. This eliminates 3 seconds per question.
🆠Topper Secret #4
For "Only" statements: instantly reverse them. "Only A are B" → "All B are A". "Only a few A are B" → "Some A are B and Some A are not B". Practice this conversion until it's automatic.